Reverberation in Rooms

Abstract

Reverberation is a typical auditory event in the time domain. Assuming a random superposition, the exponential and Rayleigh distributions are derived for the sound energy and amplitude distributions in a room indicating that the sound field is no longer uniform. Reverberation decay curves and modulation transfer functions can be derived from the impulse responses at observation points in a room assuming white noise as a source signal. Reverberation can be represented as a random process for the collisions of waves with the surrounding walls, assuming that the sound field is a superposition of sinusoidal waves with random magnitude and phase. Assuming a stochastic model for collisions and the energy balance equation in the sound field, various types of reverberation formulae are derived. Most of those formulae feature exponentially decay of reverberation in a room. In addition to the stochastic model, this chapter describes the non-exponentially decaying reverberation that can often be heard in a room, assuming that the sound field is a mixture composed of three-, two-, and one-dimensional sound fields. Interestingly, from a theoretical perspective, the energy decay does not take an exponential form, even if the sound field is purely one or two dimensional. Very steep initial decays show a 1 / t or $1/t^2$ time dependence rather than the exponential form in the one- or two-dimensional field.